One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations.
Résumé
This article presents some qualitative results for solutions of the fully nonlinear elliptic equation F(∇u,D2u) + f(u) = 0 in IRN. Precisely under some additional assumptions on f, if −1 ≤ u ≤ 1 and limx1→±∞ u(x1,x′) = ±1 uniformly with respect to x′, then the solution depends only on x1.
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